Question 972110
velocity(v) is defined as the first derivative of the position function
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h(t) = 2t(20 − t) = 40t - 2t^2
note that this is a parabola that opens downward
v = h'(t) = 40 - 4t
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a) v = h'(t) = 40 - 4t
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b) v = 40 - (4*4) = 24
ball is rising
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c) 0 = 40 - 4t
-4t = -40
t = 10 and
h(10) = 40t - 2t^2
h(10) = 400 - 200 = 200
max height is 200 m
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d) 0 = 40t - 2t^2
2t^2 = 40t
t = 20 and
h'(20) = 40 - 4*20
h'(20) = -40 which is a downward velocity of 40 m/s